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MathGroup Archive 2005

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Re: NSolve Vs. Elliptic Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62605] Re: NSolve Vs. Elliptic Integral
  • From: "nilaakash at gmail.com" <nilaakash at gmail.com>
  • Date: Tue, 29 Nov 2005 04:45:21 -0500 (EST)
  • References: <dme6pg$i69$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear All,
               Thanks everybody to answer my question. Though I have
got my answer still there are some prblems.
                Basically I wanted to get a particulam "m" value for
fixed g[m] value. Mr. Valeri and Mr. Bob both have given nice answer.
                Now if I change my g[m] value, means if I increase
g[m], the "m" value reaches close Pi/2 and the integral diverges there.
As my integral function is symmetric about Pi/2 axis, when I ask to
evaluate "m" value near Pi/2 region suddenly it jumps from left side
curve to right side curve, and I get jump.
                I am giving the code and please suggest me how to get
 those "m" values which are belong to curve which is only extended
from 0.003 to Pi/2.

Clear[f,g];

f[x_,m_]:=Sqrt[(1+0.176*Sin[m]^2*Sin[x]^2)*
        (1+1.01769*Sin[m]^2*Sin[x]^2)/(1-Sin[m]^2*Sin[x]^2)];

g[m_]:=W*46381*10^(-6)*Sqrt[1/(-0.0012245+Sin[m]^2)];

h[m_?NumericQ] := NIntegrate[f[x, m], {x, ArcSin[0.002/Sin[m]],Pi/2}]

t={};For[W = 1, W <= 400, W = W + 1,
a = FindRoot[h[m]==g[m], {m, 0.1}];
num = m /. a;
t=Join[t,Table[{num,W},{i,1,1}]];]
MatrixForm[t]

ListPlot[t, PlotRange -> All, PlotRange -> All, PlotJoined -> False,
    Frame -> True, PlotStyle -> {PointSize[0.008], Hue[0.6]}];

Thanks.

nilaakash


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